This video from startcooking.com will show you how to make easy Rudolf's Christmas Cookies. They're a little different - no flour or eggs. If you use sweetened condensed soy milk instead of the conventional version, these could easily be vegan. Of course switching out all the ingredients to their organic versions would make them organic cookies.
These cookies can be made with even the youngest children, and they'll get a kick out of putting Rudolph's nose on. If I were to make these cookies, I would only use red candied cherries (oh, hey, not sure if you can get organic versions of those; however, you could make them yourself using this recipe), and forgo the green ones. Any child over the age of two will be quick to point out to you that Rudolf did not have a green nose.